A288275 a(n) is the number of rooted maps with n edges and 5 faces on an orientable surface of genus 4.

111159740692, 10743797911132, 517592962672296, 16789118602155860, 415691294404230748, 8419549939292302908, 145737674581607574840, 2221381417843144801098, 30468100266480917147760, 382217975972687580876304, 4441222132558609054169216, 48280421251792089554320464

Offset: 12

Author

Gheorghe Coserea, Jun 08 2017

Keywords

• nonn

Links

• Sean R. Carrell, Guillaume Chapuy, Simple recurrence formulas to count maps on orientable surfaces, arXiv:1402.6300 [math.CO], 2014.

Crossrefs

Rooted maps of genus 4 with n edges and f faces for 1<=f<=10: A288271 f=1, A288272 f=2, A288273 f=3, A288274 f=4, this sequence, A288276 f=6, A288277 f=7, A288278 f=8, A288279 f=9, A288280 f=10.

Column 5 of A269924.

Cf. A000108.

Programs

Mathematica

Q[0, 1, 0] = 1; Q[n_, f_, g_] /; n < 0 || f < 0 || g < 0 = 0;
Q[n_, f_, g_] := Q[n, f, g] = 6/(n + 1) ((2n - 1)/3 Q[n - 1, f, g] + (2n - 1)/3 Q[n - 1, f - 1, g] + (2n - 3) (2n - 2) (2n - 1)/12 Q[n - 2, f, g - 1] + 1/2 Sum[l = n - k; Sum[v = f - u; Sum[j = g - i; Boole[l >= 1 && v >= 1 && j >= 0] (2k - 1) (2l - 1) Q[k - 1, u, i] Q[l - 1, v, j], {i, 0, g}], {u, 1, f}], {k, 1, n}]);
a[n_] := Q[n, 5, 4];
Table[a[n], {n, 12, 23}] (* Jean-François Alcover, Oct 16 2018 *)

Formula

G.f.: -2*y*(y-1)^12*(33259798737*y^11 + 1329990099093*y^10 + 9262655718313*y^9 + 2336641955449*y^8 - 47227883527259*y^7 + 17056753299711*y^6 + 58186472373731*y^5 - 48817840576153*y^4 + 819511081872*y^3 + 9462230411332*y^2 - 2475017890416*y + 88807125936)/(y-2)^35, where y=A000108(x).